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Vacancy formation enthalpy in γ cerium from positron annihilation
Volume 73A, number 3
PHYSICS LETTERS
17 September 1979
VACANCY FORMATION ENTHALPY IN 7CERIUM FROM POSITRON ANNIHILATION M. BOIDRON CEN/FAR-DECPu/SEAMA, 92260 Fontenay aux Roses, France
and R. PAULIN INS TN, 91190 Gifsur Yvette, France Received 21 May 1979
A vacancy formation energy of 0.72 ±0.07 eV is measured for ‘y cerium. The positron trapping observed in the ‘y’ surface film is attributed to Ce vacancies bound to oxygen with energy Eb 0.2 ±0.05 eV.
There is actually no measurement of vacancy formation enthalpy in rare earth metals excepted for lanthanurn where a value has been estimated from heat capacity data [1] by neglecting the anharmonicity contribution. It is to evaluate in what extent such measurements can be performed by using the positron annihilation method that the present investigation in fcc ‘y cerium has been undertaken. To probe the rare earth vacancies with positrons, a necessary condition is that these vacancies act as efficient positron traps where the annthilation characteristics are significantly changed compared to the metal bulk [2] Then the presence of vacancies can be detected as an increase of the positron lifetime or as a narrowing of the angular (or energetic) distribution of annihilation ‘y quanta. We study here how the angular distribution of ‘y quanta is changed when vacancies are thermally created in cerium. 64Cu source, after The positrons from a 1 Ci foil, penetrate passing through a emitted 10 pm molybdenum into a 3N cerium block of 12 X 10 X 10mm3 where they annihilate. That block in which the metallic impurities are less than 600 ppm was polished before and annealed under vacuum during 30 h at 600°Cboth to remove dislocations and to form a nearly saturated surface film of the so called 7 phase [3] The thickness of the y layer so formed is about 10 pm and does not significantly increase during the experiment. The two -
.
200
7 rays resulting from annihilation are detected in coincidence through the long collimating slits of a conventional angular correlation apparatus [4] by two NaI(Tl) scintillators with an angular resolution of l0~ rad. The Ce sample can be heated under a dynamic vacuum of lO~~ Torr with a tungsten wire insulated by alumina. Its temperature is controlled by two chromel—alumel thermocouples located at 1 mm from the face exposed to the positron flux. At every temperature the peak counting rate h of the angular correlation curve is measured to parametrise the curve narrowing for a present number of annihilation events recorded by the detector used as monitor. The variations of h with temperature resulting from five runs performed by heating and cooling for three different samples are shown in fig. 1 where the increase of h expected from the lattice expansion is also indicated. These datasample reveal awhich clear does effectnot of saturate positronbefore trapping in the cerium the phase transition fcc cc, occurring at 720°C.In addition, a fast variation around 200°Cleveling off at 300°Cis well resolved. Similar low temperature effects have sometimes been observed in other metals [5,7] where they were tentatively interpreted as evidence of positron self-trapping. In the present case, however, positron trapping by vacancies created in the 7 phase at a lower temperature than in the 7 phase seems a more realistic hypothesis. To test that hypothesis, we -~
Volume 73A, number 3
PHYSICS LETTERS .1°/el I
Thickness (pm)
T=600°C
+
CE R IUM
~ 1.10
17 September 1979
2
—-_‘---
-°
1 • 0 ~
,y4
z
°
too
°
1
10
.-°°
7<.
~
D 215°C
i~
~‘
5
~0
100
200
300 400 500 600 700t 800 Temperature 1°C) ~f.c.c ~c.c
Fig. 1. Relative intensity measured at the peak of the angular correlation curve versus temperature when positrons annihilate in cerium samples annealed 16 h at 600°C. Dotted lines mdicate the phase transition ~ —÷ ~ and the effect expected from thermal expansion of the lattice.
CERIUM 1~0
I 0
20 15
____~—
-~
1~0
Time (hours) -
Fig. 2. Growth kinetics of7 surface layer as detected in situ from the variations at the peak of the angular correlation curve versus time during isothermal annealing ofcerium (circles). Thickness of the y’ layer formed after annealing (squares and diamonds) measured by successive abrasions and X diffraction control.
have studied the appearance of the 7’ phase when just polished Ce samples are annealed under 1 0~Torr at various temperatures. The signal characteristic of X-ray diffraction in the 7 phase disappears after removing a 3 pm layer from a sample annealed during 16 h at 215°C.The layer to be removed in order to suppress the diffraction signal is three times thicker after annealing at 3 15°Cduring the same time. Even after annealing during 140 hat 600°C,the 7’ surface film does not exceed 20 pm. Since the 7’ phase grows three times faster at 315°Cthan at 215°C,the total number
perature and remains constant at higher temperatures where the trapping effect due to the 7 phase is detected. To estimate the vacancy formation enthalpies, the trapping model has only been used for the 7 phase where the data are abundant enough. In that model, the vacancy concentration is simply correlated to h as h \/(h h) r eS/Ke_~’1v11~T (1) ‘ ci V cPv where hc and h~are the h values for the bulk and the vacancy, Tc is the positron lifetime in the bulk, /1~, the trapping rate of a vacancy, k the Boltzmann constant, T the temperature, S and E1 v the vacancy formation
of vacancies able to trap positrons in that phase will also increase faster. Continuous measurements of the h parameter during isothermal annealing at these two temperatures should distinguish the two different increases of vacancy populations if the starting hypothesis is correct. The result of that experimental test is shown in fig. 2 (left part) where the other data relative to the development of the 7’ phase are also presented. The expected difference between the growth kinetics of the 7’ phase at 215 and 3 15°Cis well resolved by in situ measurements of the h parameter and thus the advanced hypothesis is confirmed, The quantitative analysis of the data relative to the annealed sample (fig. 1) has then been performed by assuming that after correction for the lattice expansion, the h value at 300°Ccorresponds to a pure trapping effect in the 7 phase. This effect saturates at that tern-
entropy and enthalpy, respectively. h (300°C)is choosen as h~while various values equal to or larger than h(660°C)are tried as hv to fit the data between 300 and 600°C.The best fIt is obtained for Eiv = 0.72 ±0.07 eV. Semi-empirical methods have also been proposed to estimated E1~in pure metals from a threshold temperature marking the deviation of the (hT) curve from the thermal expansion. We used three of them [8—10]to estimate E1~in the 7 phase. The values so found, 0.76 ±0.02,0.82 ±0.03 and 0.81 ±0.02, are very close to half the self-diffusion energy in cerium, ~ESD = 0.79 eV. Below 300°C,fitting of the h (T) curve by the trapping model is not very significant; this is why we only used the empirical methods to obtain a crude estimate of (Eiv)y’. The values found, 0.65, 0.58, 0.58 ±0.03 eV, indicate a mean difference between the two phases (E1~)7 (Eiv).y’ = 0.2 ±0.05
—
—
‘.
—
201
Volume 73A, number 3
PHYSICS LETTERS
eV. That difference can be reasonably interpreted as reflecting the binding energy of Ce vacancies with impurities present in the 7 layer. If as advanced by Gschneidner and Waber [11] oxygen is the preponderant impurity in that layer, it is instructive to estimate the binding energy Eb of the complex Ce vacancy— oxygen impurity. We use for that estimation the simple approach proposed by Quéré [121 for trivalent metals,
Eb
—0.01Z1Z2 eV,
(2)
where Z1 is the valency of the vacancy and Z2 the impurity valency both measured relatively to the bulk. For oxygen Z2 = —5 so that eq. (2) yields Eb = —0.15 eV, a value close enough to the enthalpy difference measured to indicate that positron trapping by such a cornplex is a reasonable hypothesis. The absence of positron trapping in cerium concluded from preliminary lifetime experiments [13] has been carefully reexamined by one of us [141 These new lifetime measurements show a trapping effect between 300 and 600°Cin agreement with the present data. The lifetime variation observed is small, ~r = 15 ps, but ten times larger than the thermal expansion which is measured with accuracy 58Co between 22 and 300°Cby the use of an internal positron source [15] insensitive to the 1’ phase. The present investigation is the first evidence that positron annihilation is a sensitive method to probe vacancies in rare earth metals. Moreover, it offers a strong support for the presumption of a vacancy dif-
202
17 September 1979
fusion mechanism in cerium where this problem has given rise to controversy [16, 171 References [1] A.!. Akimov and Y.A.
Krastmaker, Phys. Stat. Sol. B42 (1970) K41. [21 W. Brandt, Appl. Phys. 5 (1974) 1, and references cited therein. [3] R.T. Weiner and G.V. Raynor, J. Less. Common Metals 1(1959) 309. [4] G. Coussot and R. Paulin, J. Appl. Phys. 43(1972)1325. [5] D. Segers, L. Dorikens-Vanpraet and M. Dorikens, App). Phys. 13(1977)51. [6] K. Maier, H. Metz, D. Herlach, H. Schaefer and A.
Seeger, Phys. Rev. Lett. 39 (1977) 484. [7] D. Herlach et al., Appl. Phys; 12 (1977) 59. [8] I.K. McKenzie and P.C. Lichtenberger, Appl. Phys. 9 (1976) 331. [9] K. Kuribayashi, S. Tanigawa, S. Nanao and M. Doyama, Solid State Commun. 12 (1973) 1179. [10] S. Nanao, K. Kuribayashi, S. Tanigawa and M. Doyama, J. Phys. F7 (1977) 8. [11] K.A. Gschneidner and J.T. Waber, J. Less Common Metals 6 (1964) 354. [121 Y. Quéré, Défauts ponctuels dansles solides (Masson, Paris, 1967) p. 74. [13] These Orsay (1976), rapp. CEA R4926. [14] G. M. Marbach, Boidron and B. George, to be published. [15] C. Janot, B. George and M. Boidron, J. Phys. 40 39. [161 (1978) M.P. Dariel, D. Dayan and A. Languille, Phys. Rev. B4 (1971) 4348. [171G. Marbach, M. Fromont and D. Calais, J. Phys. Chem. Solids 37 (1976) 689.
PHYSICS LETTERS
17 September 1979
VACANCY FORMATION ENTHALPY IN 7CERIUM FROM POSITRON ANNIHILATION M. BOIDRON CEN/FAR-DECPu/SEAMA, 92260 Fontenay aux Roses, France
and R. PAULIN INS TN, 91190 Gifsur Yvette, France Received 21 May 1979
A vacancy formation energy of 0.72 ±0.07 eV is measured for ‘y cerium. The positron trapping observed in the ‘y’ surface film is attributed to Ce vacancies bound to oxygen with energy Eb 0.2 ±0.05 eV.
There is actually no measurement of vacancy formation enthalpy in rare earth metals excepted for lanthanurn where a value has been estimated from heat capacity data [1] by neglecting the anharmonicity contribution. It is to evaluate in what extent such measurements can be performed by using the positron annihilation method that the present investigation in fcc ‘y cerium has been undertaken. To probe the rare earth vacancies with positrons, a necessary condition is that these vacancies act as efficient positron traps where the annthilation characteristics are significantly changed compared to the metal bulk [2] Then the presence of vacancies can be detected as an increase of the positron lifetime or as a narrowing of the angular (or energetic) distribution of annihilation ‘y quanta. We study here how the angular distribution of ‘y quanta is changed when vacancies are thermally created in cerium. 64Cu source, after The positrons from a 1 Ci foil, penetrate passing through a emitted 10 pm molybdenum into a 3N cerium block of 12 X 10 X 10mm3 where they annihilate. That block in which the metallic impurities are less than 600 ppm was polished before and annealed under vacuum during 30 h at 600°Cboth to remove dislocations and to form a nearly saturated surface film of the so called 7 phase [3] The thickness of the y layer so formed is about 10 pm and does not significantly increase during the experiment. The two -
.
200
7 rays resulting from annihilation are detected in coincidence through the long collimating slits of a conventional angular correlation apparatus [4] by two NaI(Tl) scintillators with an angular resolution of l0~ rad. The Ce sample can be heated under a dynamic vacuum of lO~~ Torr with a tungsten wire insulated by alumina. Its temperature is controlled by two chromel—alumel thermocouples located at 1 mm from the face exposed to the positron flux. At every temperature the peak counting rate h of the angular correlation curve is measured to parametrise the curve narrowing for a present number of annihilation events recorded by the detector used as monitor. The variations of h with temperature resulting from five runs performed by heating and cooling for three different samples are shown in fig. 1 where the increase of h expected from the lattice expansion is also indicated. These datasample reveal awhich clear does effectnot of saturate positronbefore trapping in the cerium the phase transition fcc cc, occurring at 720°C.In addition, a fast variation around 200°Cleveling off at 300°Cis well resolved. Similar low temperature effects have sometimes been observed in other metals [5,7] where they were tentatively interpreted as evidence of positron self-trapping. In the present case, however, positron trapping by vacancies created in the 7 phase at a lower temperature than in the 7 phase seems a more realistic hypothesis. To test that hypothesis, we -~
Volume 73A, number 3
PHYSICS LETTERS .1°/el I
Thickness (pm)
T=600°C
+
CE R IUM
~ 1.10
17 September 1979
2
—-_‘---
-°
1 • 0 ~
,y4
z
°
too
°
1
10
.-°°
7<.
~
D 215°C
i~
~‘
5
~0
100
200
300 400 500 600 700t 800 Temperature 1°C) ~f.c.c ~c.c
Fig. 1. Relative intensity measured at the peak of the angular correlation curve versus temperature when positrons annihilate in cerium samples annealed 16 h at 600°C. Dotted lines mdicate the phase transition ~ —÷ ~ and the effect expected from thermal expansion of the lattice.
CERIUM 1~0
I 0
20 15
____~—
-~
1~0
Time (hours) -
Fig. 2. Growth kinetics of7 surface layer as detected in situ from the variations at the peak of the angular correlation curve versus time during isothermal annealing ofcerium (circles). Thickness of the y’ layer formed after annealing (squares and diamonds) measured by successive abrasions and X diffraction control.
have studied the appearance of the 7’ phase when just polished Ce samples are annealed under 1 0~Torr at various temperatures. The signal characteristic of X-ray diffraction in the 7 phase disappears after removing a 3 pm layer from a sample annealed during 16 h at 215°C.The layer to be removed in order to suppress the diffraction signal is three times thicker after annealing at 3 15°Cduring the same time. Even after annealing during 140 hat 600°C,the 7’ surface film does not exceed 20 pm. Since the 7’ phase grows three times faster at 315°Cthan at 215°C,the total number
perature and remains constant at higher temperatures where the trapping effect due to the 7 phase is detected. To estimate the vacancy formation enthalpies, the trapping model has only been used for the 7 phase where the data are abundant enough. In that model, the vacancy concentration is simply correlated to h as h \/(h h) r eS/Ke_~’1v11~T (1) ‘ ci V cPv where hc and h~are the h values for the bulk and the vacancy, Tc is the positron lifetime in the bulk, /1~, the trapping rate of a vacancy, k the Boltzmann constant, T the temperature, S and E1 v the vacancy formation
of vacancies able to trap positrons in that phase will also increase faster. Continuous measurements of the h parameter during isothermal annealing at these two temperatures should distinguish the two different increases of vacancy populations if the starting hypothesis is correct. The result of that experimental test is shown in fig. 2 (left part) where the other data relative to the development of the 7’ phase are also presented. The expected difference between the growth kinetics of the 7’ phase at 215 and 3 15°Cis well resolved by in situ measurements of the h parameter and thus the advanced hypothesis is confirmed, The quantitative analysis of the data relative to the annealed sample (fig. 1) has then been performed by assuming that after correction for the lattice expansion, the h value at 300°Ccorresponds to a pure trapping effect in the 7 phase. This effect saturates at that tern-
entropy and enthalpy, respectively. h (300°C)is choosen as h~while various values equal to or larger than h(660°C)are tried as hv to fit the data between 300 and 600°C.The best fIt is obtained for Eiv = 0.72 ±0.07 eV. Semi-empirical methods have also been proposed to estimated E1~in pure metals from a threshold temperature marking the deviation of the (hT) curve from the thermal expansion. We used three of them [8—10]to estimate E1~in the 7 phase. The values so found, 0.76 ±0.02,0.82 ±0.03 and 0.81 ±0.02, are very close to half the self-diffusion energy in cerium, ~ESD = 0.79 eV. Below 300°C,fitting of the h (T) curve by the trapping model is not very significant; this is why we only used the empirical methods to obtain a crude estimate of (Eiv)y’. The values found, 0.65, 0.58, 0.58 ±0.03 eV, indicate a mean difference between the two phases (E1~)7 (Eiv).y’ = 0.2 ±0.05
—
—
‘.
—
201
Volume 73A, number 3
PHYSICS LETTERS
eV. That difference can be reasonably interpreted as reflecting the binding energy of Ce vacancies with impurities present in the 7 layer. If as advanced by Gschneidner and Waber [11] oxygen is the preponderant impurity in that layer, it is instructive to estimate the binding energy Eb of the complex Ce vacancy— oxygen impurity. We use for that estimation the simple approach proposed by Quéré [121 for trivalent metals,
Eb
—0.01Z1Z2 eV,
(2)
where Z1 is the valency of the vacancy and Z2 the impurity valency both measured relatively to the bulk. For oxygen Z2 = —5 so that eq. (2) yields Eb = —0.15 eV, a value close enough to the enthalpy difference measured to indicate that positron trapping by such a cornplex is a reasonable hypothesis. The absence of positron trapping in cerium concluded from preliminary lifetime experiments [13] has been carefully reexamined by one of us [141 These new lifetime measurements show a trapping effect between 300 and 600°Cin agreement with the present data. The lifetime variation observed is small, ~r = 15 ps, but ten times larger than the thermal expansion which is measured with accuracy 58Co between 22 and 300°Cby the use of an internal positron source [15] insensitive to the 1’ phase. The present investigation is the first evidence that positron annihilation is a sensitive method to probe vacancies in rare earth metals. Moreover, it offers a strong support for the presumption of a vacancy dif-
202
17 September 1979
fusion mechanism in cerium where this problem has given rise to controversy [16, 171 References [1] A.!. Akimov and Y.A.
Krastmaker, Phys. Stat. Sol. B42 (1970) K41. [21 W. Brandt, Appl. Phys. 5 (1974) 1, and references cited therein. [3] R.T. Weiner and G.V. Raynor, J. Less. Common Metals 1(1959) 309. [4] G. Coussot and R. Paulin, J. Appl. Phys. 43(1972)1325. [5] D. Segers, L. Dorikens-Vanpraet and M. Dorikens, App). Phys. 13(1977)51. [6] K. Maier, H. Metz, D. Herlach, H. Schaefer and A.
Seeger, Phys. Rev. Lett. 39 (1977) 484. [7] D. Herlach et al., Appl. Phys; 12 (1977) 59. [8] I.K. McKenzie and P.C. Lichtenberger, Appl. Phys. 9 (1976) 331. [9] K. Kuribayashi, S. Tanigawa, S. Nanao and M. Doyama, Solid State Commun. 12 (1973) 1179. [10] S. Nanao, K. Kuribayashi, S. Tanigawa and M. Doyama, J. Phys. F7 (1977) 8. [11] K.A. Gschneidner and J.T. Waber, J. Less Common Metals 6 (1964) 354. [121 Y. Quéré, Défauts ponctuels dansles solides (Masson, Paris, 1967) p. 74. [13] These Orsay (1976), rapp. CEA R4926. [14] G. M. Marbach, Boidron and B. George, to be published. [15] C. Janot, B. George and M. Boidron, J. Phys. 40 39. [161 (1978) M.P. Dariel, D. Dayan and A. Languille, Phys. Rev. B4 (1971) 4348. [171G. Marbach, M. Fromont and D. Calais, J. Phys. Chem. Solids 37 (1976) 689.